Either your light switch has died or the fusebox is melting where the dim-dip relays go.

To check the relays, take the fusebox lid off, and in the back right corner (looking from the front of the car) is a pack of small 10A relays (white, brown and blue). Lift these out, and one will have charred marks either on the bottom of it, or the plastic of the fusebox will be melted slightly.

It is a common problem, especially if you use uprated bulbs (or some cheap ones).